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AFR conditions under deceleration

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What should the AFR conditions look like under deceleration? Some cars go full lean and some stay at 14.7 and some go rich and I'm wondering what are the advantages and disadvantages to different decel AFR conditions?

General principles:

Full fuel cut is for fuel saving. Any situation where it could be fuel cutting but it's not (assuming it's not some bad tuning or mechanical problem) is to address driveability/smoothness or emissions.

Standalone ECUs have simpler fuel cut controls. They're generally just cutting all cylinders based on pedal/throttle position thresholds, and recovering from fuel cut based on RPMs.

Stock ECUs are all over the place. They tend to have much more sophisticated controls for decel fuel cut and fuel cut recovery. In terms of cut in and cut out, they might cut in stages: half cylinders first, then the other half.

From a perspective of AFR, they might intentionally spike rich for a moment on tip in or tip out, usually as an emissions thing (keep the cat from getting too much oxygen and making NOx emission).

They may have more specific fuel cut inhibit conditions for smoothness or emissions based on temperature, gear position, etc. That's where you see the 14.7 instead of a fuel cut.

Alright so if you aren't considering emissions or fuel consumption and you are focusing on power and safety for the engine, would the optimal condition be a 14.7 AFR rather than a fuel cut to keep cylinder temps down under deceleration?

Engine runs coolest when there is no combustion (it's just a moving airpump), so shutting fuel will cool things down better. Just cut fuel whenever you can, being mindful of driveability. Deceleration fuel cut isn't going to damage anything.

Awesome thank you!